Flaws in the Letter Grade System

       What does it mean when you get an A in a class?  I'm not asking, "What is it supposed to mean?"  I'm asking, "What does it actually mean?"  Does the "A" in Chemistry mean the same as the "A" in History?  Does the "A" in Physical Education mean the same as the "A" in English?  What does a "B" mean; what does a "D" mean?  Did you ever get an "A" in a class--middle school, high school, or college--and then brag to your friends that you didn't learn a thing?  Did you ever get an "A" or a "B" in a class and fail the final exam?  Did you know someone who consistently earned "A's" and "B's" in math classes and couldn't score over 500 on the math portion of the SATs?

       Howard Pitler list four major problems with our current system of using letter grades:

1. There is no consistency from teacher to teacher or from school to school.  Schools and school districts may have different policies about grading; and these policies aren't necessarily the same from school to school or from school district to school district.
2. Teachers decide the factors that go into a course grade and they decide the weighting for each of these factors.  So called "hard teachers" and "easy teachers" is actually a real thing when it comes to grading in the letter grading system.  Some teachers are more demanding than others; some teachers award "points" for non-academic behaviors such as showing up to class on time or not using all of your allotted bathroom passes. Merely completing homework can be part of the grade regardless of the quality or the "learning" that may have occurred while completing the homework.
3. Grades discourage students from learning.  Pitler quotes Alfie Kohn who says, 

 “Kids who are graded—and have been encouraged to try to improve their grades—tend to lose interest in the learning itself, avoid challenging tasks whenever possible (in order to maximize the chance of getting an A), and think less deeply than kids who aren’t graded.” The target becomes the grade rather than the learning. Students take less challenging classes because they want to “protect” their GPAs.

 4.  Lastly, true learning often requires multiple attempts in which ultimate success doesn't happen until the end of the process.  When students are more concerned about "getting grades", they tend to try less, they are less willing to go through the necessary struggle needed to achieve the ultimate level of true learning.

       There is another way to measure student learning and that is to compare their learning against standards (or proficiencies or competencies) that everyone can agree on.  Proficiency-based Learning is not new.  In fact it is growing in popularity among educators who want students and parents to have a better understanding of the actual learning that is taking place in our schools.  One of the hallmarks of proficiency-based learning is the idea that students need time to re-visit topics and ideas in their journey toward true learning and true understanding.  Hence, assessments are used to help students and parents to "see" the learning that occurred and to recognize the learning that still needs to happen.  When students are re-assessed, grades aren't averaged.  Instead, higher grades at a later time in the learning process are recognized as the actual level of learning that occurred.  Therefore, students are encouraged to try harder.

       Proficiency-based Learning should also allow students to work at their own pace.  Ideally, they should not move on to something new until they have a good understanding of the current lesson or idea or standard.  Also, students may have opportunities to demonstrate their understanding in multiple ways; not always via a summative test--however these tests can be still be used.

       Schools are for learning, not for "getting grades".  And we need to have a better system for identifying the learning that takes place.  Too many students are graduating from high school without the skills to hold a job or complete college or make good decisions for themselves.  We need to do better for our students so that they will have better options for their futures.

Why Is Teaching Mathematics So Different Than Teaching Other Subjects?

       My entire professional career has been in Secondary Mathematics.  As a middle school teacher, high school teachers, department chair, and supervisor; I have been immersed in the field of teaching and learning mathematics.  Whenever conversations arise about the instruction for very weak students or for very advanced students, there seems to always be special considerations for students when it comes to mathematics.  Principals, school counselors, and special educator alike all agree that the teaching and learning of mathematics seem to require very different skills compared to the teaching and learning of reading and history and (perhaps) other subjects.

       Keith Devlin has a relatively simple answer to this question which he explains in his paper written for the Mathematical Association of America titled, In Math You Have to Remember, In Other Subjects You Can Think About It.  Devlin explains that mathematics is often taught as a series of rules that you just have to memorize.  Whereas other subjects such as history and science are taught within a context that help the learner to make sense of the content.  Mathematics could be taught within a context (and, I would say SHOULD be taught within a context), but it usually isn't.  This makes mathematics seem like a secret language with tricks and complicated rules that sometimes work in some situations and don't work in other situations.  When mathematics is taught as merely a bunch of skills without any understanding of how and when to use these skills, many students struggle to be successful.


       In her book Mathematical Mindsets, Stanford professor Jo Boaler explains that all students can learn mathematics if teachers are equipped to help students to build understanding.  While it is relatively easy for trained secondary mathematics teachers to learn these techniques, most teachers have not received this training when they were in college.  Furthermore, most adults today (parents, school principals, school counselors, etc) grew up learning mathematics through a strictly procedural approach.  Because of this experience, most adults believe that mathematics should be taught as a bunch of skills.

       Fortunately, more and more teachers are mixing more and more conceptual understanding in their mathematics classrooms along with learning the skills.  There are places in which math is taught somewhat differently than it was taught in past generations, and this is a good thing in my opinion even if it makes some parents feel uncomfortable.  Math should not be taught as 100% skills without any connection to the real world.  For most students, this sort of instruction is just too abstract for them to understand.


       Mathematics is also a subject that builds on itself from school year to school year.  Students need to have a good understanding of the concepts so that they can build on previously learned content to understand the new content.  This idea of building from year to year is more prevalent in mathematics than it is in other subject areas.

When Learning Doesn't Happen, Who's Fault Is It?

       When something goes wrong, is it your fault or is it someone else's fault?

       You're late to work, you fail a class, you break a shoelace, you gain weight, you run out of milk.  Small things and big things; they happen every day.  Are you the kind of person that says, "It's my fault." most of the time when things go wrong; or are you the kind of person who says (essentially), "It's someone else's fault." most of the time when things go wrong.

       Maybe this isn't a fair question.  Certainly there are times when it is my fault and times when it is someone else's fault.  You can't answer such an abstract question with a definitive answer one way or the other.  Well, OK.  Maybe so.  But surely you know someone who almost never takes responsibility for anything that happens in their life.  When they are late to work; it's because of slow drivers and red traffic lights.  When they gain weight; it's because other people are constantly offering them sweets.  When they lose a game of cards; it's because the cards weren't shuffled well.

       When middle and high school students struggle to learn in school; Who's fault is it?  Who is ultimately responsible for their learning?  Who bears the greatest ownership for whether or not they learn math and English and science?  There is no doubt that this is a controversial question.  This is a question in which any answer would have troublesome consequences.  Another way to ask this question is, "Do we blame the schools, or blame the students?"  Unfair you say?  Maybe.  Probably.  But this is a question that educators get often.  I am going to begin by looking at the extreme answers.

1) It's the student's fault

       This view says that students bear the ultimate responsibility for their own learning.  The teacher's job is to teach.  It is the student's job to learn.  If the student isn't learning, they should seek extra help; they should ask questions; they should try harder.  Middle and high school children aren't babies; they understand how school "works".  They should advocate for themselves.  It's their life.

       The problem with this view, in my opinion, is the question of age-appropriate responsibility that is given to students.  My father used to say that the trouble with kids is that they act their age.  In addition to learning math and English and science, students are also learning how to be an adult.  They are learning about making good decisions.  Teenagers need structure; they need guidelines.  Sometimes a student is struggling in a subject and doesn't know what questions to ask.  Sometimes students are afraid to speak up in class in front of their peers.  Sometimes students don't realize the ramifications of not learning.  While, of course we want our students to be responsible for their own learning, we can't expect an 11 year-old 6th graders nor a 15 year-old 10th grader to act like a fully responsible adult at all times.

2) It's the teacher's fault

       This view says, if students aren't learning, then the teacher isn't doing his/her job.  Teachers are trained to teach and to help students to learn.  The teachers went to college to learn how to teach and they spent two or more years as full-time, untenured teachers to learn "in the field".  If students aren't learning, then it's the teachers fault.

       The problem with this view, (again) in my opinion, is the idea that all students learn in the same way; or that teachers should be experts in all student learning styles after a couple of years of practice.  In fact, students are very, very different in their learning styles.  Some learn from only listening, while others have to listen and practice, while others have to hear it in a different way before they "get it".  Middle and high school students have varied past experiences in their education and teachers are always faced with students of varying abilities.  Some students don't speak up much and teachers have to find a way to understand how well they are catching on to the learning objectives without hearing (verbally) directly from the student.  And some students are burdened with problems at home that have priority over their education in the student's mind.

     

       So who's fault is it?  If we can't say it's the student's fault and we can't say it's the teachers fault (and we still have learning that isn't happening) then who's fault is it?

       We live in a world that loves to point fingers and loves to have clear, simple "right/wrong" answers.  We want to have a villain that we can point to; someone to blame; someone to yell at.  Everything is a soccer game with winners and losers.  We don't like complicated things, complex things.  These are too hard to understand and too hard to fight.

       Who's fault is it?  I think it depends on the person that you are.  If you are the type to take responsibility for your actions, then you probably lean toward the side that says students should be responsible for their own learning.  If you are the type to blame others and nothing is ever your fault, then you probably lean toward the side that says the teachers and the schools are to blame.  As for me--and as an educator--I take a middle-of-the-road view.  Sure we want students to be responsible, but teachers should do everything that they can to help students to learn.  It's not enough to just "teach".  If students aren't learning, teachers and schools should ask why.  They should take a hard look at these students and provide whatever help they can.

       I believe that our public schools are constantly concerned about students who struggle to learn.  Most of time, these students get the help that they need.  But sometimes they don't.  In the end, as with so many things in life, I believe that we have to work together to help our most vulnerable students to get the help that they need.  Learning requires a little struggling for everyone.  For those who can't meet this struggle, we should all be there to help them.

Data, Data, Data Leading to High Achievement

     Education and learning is the result of hours of planning and hard work on the part of teachers and students.  Behind the scenes in every public school that cares about student learning, there are individual and teams of teachers that use data to make good instructional decisions.

       In years past, we only had data from chapter tests.  But since the chapter was completed and the instruction has already moved on to the next topic, this data was already "old news".  It couldn't be used to help us to make good instruction decision for right now.  Today teachers understand the power of using data to guide their decisions.  When the public hears about school data, they often think about tests results--probably because that is the most common form of data that is published in the news.  But teachers use all sorts of data that doesn't include test data.

Data-Driven Decision Making

       Public school teachers measure student progress in many ways in today's classrooms.  Teachers use rubrics to assess projects or some assignments.  Teachers use games.  Teachers use exit tickets.  Questions, discourse, group work, individual work, electronic responses, etc.  Teachers have multiple sources of student data.  This data is used to help teachers to decide:

1. Who gets it.
2. Who sort of gets it.
3. Who doesn't get it.

These determinations are used to help teachers to prepare for the next lesson.  Chapter tests and large, state-wide standardized tests are a "final" product of the educational process.  They don't help us in our day-to-day planning.  It is the daily collection of data from formative assessments that inform instructional decision.  It is also this data (or the information from this data) that help students to gain a sense of how well they are understanding the content.

       Indeed, learning is a process.  It takes time and practice and effort.  It requires students and teachers to ask a lot of questions and often to make mistakes along the way.  It requires thinking and reasoning based on what we've done so far and what we still need to do.  The data that comes from these efforts help all of us to measure progress toward the goal of learning.  Most of this data analyzing is invisible to the public.  It is the technical work of teaching that is too "un-interesting" to print in the newspapers and yet vital to the practice of teaching.

       Data drives decisions for students and schools.  Data is the fuel that keeps our classrooms running in the right direction.

Teachers Seeking Innovative Learning Strategies

       If students aren't learning, then the teacher isn't succeeding.

       This is a harsh statement.  Clearly there are lots of reasons that prevent students from learning.  Some of these reasons can be due to teacher actions in the classroom and some are outside the control of the teacher.  But the main goal of school is learning.  If the student isn't learning, than we haven't met this main goal.

       Of course, not all students learn in the same way.  When a teachers presents a lesson--be it via lecture, or a game, or discovery learning, or through the use of a task, or some combination of these methods--some students will "get it" and some will not.  And so our best teachers are constantly looking for different ways (different teaching strategies) to help students to learn.  This (indeed) is the part of teaching that very, very complex.  Trying to understand the best way to help students to learn--every student in every class--is the struggle of every teacher.

       Alas, the world of education is full of ideas to help us.  Some of these ideas fall into the category good suggestions that any teacher should use, such as:

• Scaffolding - breaking up the learning into smaller chucks and allowing students the time to learn one-piece-at-a-time in the effort to get them to learn the whole idea or standard.
• Graphic Organizers - providing students with different ways to organize information so that "many ideas or facts" are easier to see and to understand.
• Multisensory - presenting new information in multiple ways that help the students brain to store the information in multiple ways.  For instance, verbally explaining something while also writing the information on a whiteboard or computer screen, while also (perhaps) providing a manipulative or foldable for the student to hold and work with tactilely.  

Other ideas are more specific as to the sort of instructional style that may take place in a classroom.  A typical example of this would Direct Instruction or Lecture.  This is very typical in classrooms in the United States; particularly in our high schools.  Adults in their 70's and 80's probably received instruction in this manner when they were in high school and their grandchildren and great-grandchildren likely receive their high school instruction in this same mode.  Some people refer to this sort of instruction as Traditional classroom instruction--and it clearly is not effective for all students.

       More teachers are using a Discovery Learning approach to classroom instruction at least some of the time in their classes.  This approach allows students to build on past learnings by completing tasks and problems that require them to do so.  Students may work individually or in small groups of three or four while the teacher responds to students' questions and encourages students to think about other solutions.  This approach is common in some countries but is much less used in the United States.   

       I am part of a couple of math groups on Facebook and I posed the question, "Is Direct Instruction Necessary?"  I went on to ask if Discovery Learning could be the sole or major teaching strategy in a high school math class.  Of course the responses that I received were various and wide ranging, but I did learn a lot more about individuals and groups of teachers who use this approach with some success.  

       When teachers are continuously searching for more and better ways to reach their students, everyone wins: students, teachers, schools, society.

Three Cheers for Middle School!

       When I interview future mathematics teachers, some embarrassingly say to me, "I actually prefer to teach at the middle school level."  Then they go on to say that their parents and friends think that they are crazy to be a middle school teacher.  This is because so many people have this image of middle-school-aged children as being wild and out of control all of the time.  I hear this so often; sometimes in silly way and sometimes in a very serious way.  As a longtime educator I can tell you that this image is untrue and unfair to young teenagers.

       Middle school is great!  The excitement and energy of the students is part of the reason that middle schools are so great.  Our best middle school teachers understand how to use that energy to engage students and to foster learning.  When middle school students are respected and appropriately challenged academically, they rise to the occasion and show their best everyday.  Middle schools are the places where you have classes with tall girls and short boys; shy kids and talkative kids.  Middle school students are fun and interesting to get to know.  They are excited to leave their elementary school and they are anxious to go to high school.

       We want and we need teachers who understand the middle school child; understand how they think and how they learn.  Teachers who are excited to teach everyday and to help their students to discover their ability to solve problems and to ask difficult questions.  We need teachers to encourage our middle school students to read and to understand more difficult text; including non-fiction text.  Middle school is often the place in which students first encounter difficulty with their academics, so we need teachers who are excited to help these students to preserve through these difficult times and to find ways to succeed.

       I know many middle school teachers who love their job.  These teachers understand the "line" between allowing students to express themselves while keeping the class of students in control.  Middle school students understand the need for structure and appreciate teachers who insist on this structure.  Middle school can be the best years of a student's school career when they have great teachers and leaders who care about them.

       Middle school is a great place to be.  Everyone should appreciate the excitement and energy of our nation's middle schools.